MAINIDEA Write the Main Idea for this section. Explain why the slope of a velocity-time graph is the average acceleration of the object.

Transcription

1 Accelerated Motion 2 Motion with Constant Acceleration 4(A), 4(B) MAINIDEA Write the Main Idea for this section. REVIEW VOCABULARY displacement Recall and write the definition of the Review Vocabulary term. displacement Notes: Explain why the slope of a velocity-time graph is the average acceleration of the object. GET IT? Identify What physical quantities do the area under a velocity-time graph and the slope of a velocity-time graph represent? 1

2 Notes Write the equation that relates final velocity and average acceleration below. Explain what each variable means. v f = +a Use with Example Problem 3. TRY IT! Use this column for scratch work and sketches. Problem FINDING DISPLACEMENT FROM A VELOCITY-TIME GRAPH The velocitytime graph shows the motion of a car traveling at a constant velocity of m/s (forward is the positive direction). Find the displacement of the car for Δt1 = 10.0 s and for Δt2 = 20.0 s. Velocity (m/s) A t 1 A t Time (s) 1. ANALYZE AND SKETCH THE PROBLEM KNOWNS UNKNOWNS v = =? Δt1 = =? Δt2 = 2

3 Notes TRY IT! (continued) 2. SOLVE FOR THE UNKNOWN Use the relationship among displacement, velocity, and time interval to find Δx1 during Δt1 = 10.0 s. Use the same relationship to find Δx2 during Δt2 = 20.0 s. 3. EVALUATE THE ANSWER Do the signs make sense? Is the magnitude realistic? Write the equation that relates position, velocity, and constant acceleration without including time. Then, explain in words what the equation means. 3

4 Student Edition, pp. 72 Use with Example Problem 4. Use this column for scratch work and sketches. TRY IT! Problem DISPLACEMENT An automobile starts at rest and accelerates at 5.7 m/s 2 after a traffic light turns green. How far will it have gone when it is traveling at 15 m/s? 1. ANALYZE AND SKETCH THE PROBLEM KNOWNS UNKNOWN xi = =? vi = vf = a = a= 2. SOLVE FOR THE UNKNOWN Use the relationship among velocity, acceleration, and displacement to find xf. Copyright McGraw-Hill Education. Permission is granted to reproduce for classroom use. 3. EVALUATE THE ANSWER Are the units correct? Do the signs make sense? Is the magnitude realistic? 4

5 SUMMARIZE REVIEW IT! 33. MAINIDEA If you were given initial and final velocities and the constant acceleration of an object, and you were asked to find the displacement, what mathematical relationship would you use? 34. Acceleration A woman driving west along a straight road at a speed of 23 m/s sees a deer on the road ahead. She applies the brakes when she is 210 m from the deer. If the deer does not move and the car stops right before it hits the deer, what is the acceleration provided by the car s brakes? 35. Distance The airplane in Figure 18 starts from rest and accelerates east at a constant 3.00 m/s 2 for 30.0 s before leaving the ground. Δx Figure 18 a. What was the plane s displacement(δx)? b. How fast was the airplane going when it took off? 5

6 36. Distance An in-line skater first accelerates from 0.0 m/s to 5.0 m/s in 4.5 s, then continues at this constant speed for another 4.5 s. What is the total distance traveled by the in-line skater? 37. Final Velocity A plane travels a distance of m north while being accelerated uniformly from rest at the rate of 5.0 m/s 2. What final velocity does it attain? 38. Final Velocity An airplane accelerated uniformly from rest at the rate of 5.0 m/s 2 south for 14 s. What final velocity did it attain? 39. Graphs A sprinter walks up to the starting blocks at a constant speed and positions herself for the start of the race. She waits until she hears the starting pistol go off and then accelerates rapidly until she attains a constant velocity. She maintains this velocity until she crosses the finish line, and then she slows to a walk, taking more time to slow down than she did to speed up at the beginning of the race. Sketch a velocity- time and a position-time graph to represent her motion. Draw them one above the other using the same time scale. Indicate on your position-time graph where the starting blocks and finish line are. 40. Critical Thinking Describe how you could calculate the acceleration of an automobile. Specify the measuring instruments and the procedures you would use. 6